It comes after nearly 100 people took to small boats on Friday in separate attempts to traverse the English Channel.
The news prompted Home Secretary Priti Patel to seek talks with her French counterpart to address the crisis.
Mr Johnson told reporters on Friday: “Clearly the most important thing is to stop them coming across from France so we are working very closely with the French authorities.
“The point I would just make to people thinking of making this journey – one, it is very hazardous, you may think the weather looks great but it’s a very, very dangerous thing to do.
“The second thing is – we will send you back. The UK should not be regarded as a place where you could automatically come and break the law by seeking to arrive illegally.
“If you come illegally, you are an illegal migrant and I’m afraid the law will treat you as such.”
Authorities were called to at least seven incidents on Thursday involving 94 people who were trying to cross the water from France to get to the UK.
The wave of attempted crossings continued on Friday – with UK authorities understood to have been called to the Kent coast near Lydd.
Earlier in the morning, the French coastguard said 24 migrants, reportedly including seven children and a woman, were also found trying to cross the Channel.
Dover MP Charlie Elphicke said on Twitter: “Only when migrants and traffickers alike know that they will not succeed in crossing the English Channel will this crisis come to an end.”
The news comes as Ms Patel prepares to hold talks with her counterpart, the French Interior Minister Christophe Castaner, to address the crisis in the wake of Thursday’s surge of reports.